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# 数据科学代写|复杂网络代写Complex Network代考|Triple-Tuple Motif

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## 数据科学代写|复杂网络代写Complex Network代考|Triple-Tuple Motif

In the third step, we wonder the occurrence frequency of 5 sorts of triads based on the concept of $T B P s$, which can effectively and simply reflect the microstructure of GVC. If we compare the GVC to DNA, the TBPs will be its base pairs. As we mentioned above, TBP1 stands for inland trade (for instance, AUSS1 $\rightarrow$ AUSS3 $\rightarrow$ AUSS4), TBP2 for international trade I (AUSS1 $\rightarrow$ AUTS3 $\rightarrow$ AUSS4), TBP3 for import trade (AUSS1 $\rightarrow$ AUTS3 $\rightarrow$ AUTS3), TBP4 for export trade (AUSS1 $\rightarrow$ AUSS3 $\rightarrow$ AUTS3), TBP5 for international trade II (AUSS1 $\rightarrow$ AUSS3 $\rightarrow$ BELS3). In detail, all the consecutive-three-strings fragments on all the SRPLs are first identified according to the concept of $T B P s$, and then statistics of triple-tuple motifs are examined according to the names of industrial sectors and economies. For instance, we can get $\mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4$ and AUS $\rightarrow$ AUS $\rightarrow$ AUS from AUSS1 $\rightarrow$ AUSS3 $\rightarrow$ AUSS4, $\mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4$ and AUS $\rightarrow$ AUT $\rightarrow$ AUS from AUSS1 $\rightarrow$ AUTS3 $\rightarrow$ AUSS4, etc. The frequency for all the possible combinations of triad on both the national level and sectoral level can be obtained under the circumstances of five TBPs. At last, we add up the same sort of $T B P$ to produce new indicators named Cumulative Trade Brokerage Property (CTBP). Notice that, due to this cumulation process, only one set of CTBPs is obtainable.

The most obvious feature in Fig. 3.7 is the proportion of CTBP2, indicating it is rare that countries provide value-added services of intermediate goods for another one (i.e., they import intermediate goods from other countries and then export them to the same one after further processing). In contrast, it is the trend that countries also acquire industrial resources on the GVC through import and export trade (the ratio of both CTBP3 and CTBP4 is basically stable in one-third), and cooperate with upstream and downstream countries on the GVC (the ratio of CTBP5 is 23.44\%, which shows a downward tendency during 15 years) to ensure the sustainable development of the global economic system (although there has been a certain degree of anti-globalization in recent years).

From the statistics of triads on the sectoral level (see Table 3.2), the most frequent triple-tuple motifs are based on the top 5 manufacturing and services, which once again certify that the manufacturing-related IVC links constitute the GVC as the most important microstructural basis. Since the year of 2000 , the top 3 triple-tuple motifs are always SC3 $\rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3, \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 4$, and SC4 $\rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3$ However, it is scarcely seen that three industrial sectors of a triad all belong to manufacturing appears less and less, reducing from 26,105 times in 2000 to 20,633 times in 2014. The rankings of the following triple-tuple motifs are constantly changing, and the overall frequency is higher than that in 2000 . It is thus crystal clear that the global industrial structure has been in an ongoing process of adjustment. It will be further analyzed in subsequent research according to the classification of 56 sectors.

## 数据科学代写|复杂网络代写Complex Network代考|Average/Maximum Strongest Relevance Degree

In non-weighted networks, the Average Path Length (APL) of the whole network can be calculated via FWA, depicting the degree of separation of nodes. As a counterpart in GIVCN model, the average of $S R P L^{\prime}$ matrix is chosen to measure the overall flow efficiency of the economic system, i.e., the Connectedness of Industrial Value Chain. The Average Strongest Relevance Degree (ASRD) is proposed, namely:
$$A S R D=\frac{\sum_{i=1}^N \sum_{j=1}^N S R P L_{i j}^{(N)}}{N}$$
where $S R P L_{i j}^{(N)}$ is the $S R P L$ between nodes $i$ and $j$ within the scope of the whole network. We allow for self-loops, and the denominator thus incorporates two parts, i.e., edges and self-loops.
$$N=N_e+N_s=N_n\left(N_n-1\right)+N_s$$
where $N_e$ stands for the number of normal edges, $N_s$ for self-loops, and $N_n$ for nodes. Furthermore, to observe its impact on the uppermost branch of $\mathrm{GVC}$, another measuring method named the Maximum Strongest Relevance Degree (MSRD) is here designed, namely:

$$M S R D=\max {i, j \in{1,2, \cdots, N}}\left{S R P L{i j}^{(N)}\right}$$
In a mathematical sense, $M S R D$ is the highest value in $S R P L^{\prime}$ matrix, and there exists a complicated process of intermediate goods propagation behind it. Different from ASRD, MSRD only depends on a single value chain that covers the most significant spreading effect across industrial sectors-just like a threshold value of the Compactness of Industrial Value Chain. Correspondingly, both upstream and downstream sectors are respectively the source and sink nodes of this max-SRPL path. Under normal circumstances, the random small-scale industrial fluctuation is not supposed to shake the closest economic connection in the global or regional economic system, and this kind of special IVC will in turn drive the development of all relevant industrial sectors and even the entire industrial network.

## 数据科学代写|复杂网络代写Complex Network代考|Average/Maximum Strongest Relevance Degree

$$A S R D=\frac{\sum_{i=1}^N \sum_{j=1}^N S R P L_{i j}^{(N)}}{N}$$

$$N=N_e+N_s=N_n\left(N_n-1\right)+N_s$$

$$M \text { S R D }=\backslash \max {i, j \backslash \text { in }{1,2, \backslash \text { cdots, } N}} \backslash \text { left }{S R P L{i j} \wedge{(N)} \backslash \text { right }}$$

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